群塔平面优化布置问题的数学建模与求解

Mathematical Modeling and Solution of Optimal Layout of Group Tower Cranes

群塔平面布置是一个典型的工程优化问题。本文从工程施工的实践角度出发,对工程设计和施工人员所提出的群塔平面优化问题进行了深入分析,明确了塔吊平面布置问题的目标函数除了考虑塔吊租金之外,还应当考虑施工区域未覆盖和重复覆盖的影响,利用罚函数实现了多个目标的组合。对设计变量和约束条件都进行了归一化处理。对于所建立的优化数学模型,采用了具备本质并行性、全局收敛性的智能优化算法进行了求解。最后,利用本文所建立的方法对一个实际工程的群塔平面优化布置问题进行了分析求解,分别给出了塔吊数量为5、6、7时的最优布置方案,并根据工程的实际状况进行了分析。数值算例表明,本文所提出的方法具备可用性和有效性,能够解决一般的群塔平面优化布置问题。

The layout of group tower cranes is a typical engineering optimization problem.From the practical point of view of engineering construction,this paper makes an in-depth analysis of the plane optimization problem of group tower cranes proposed by engineering design and construction personnel,and clarifies that the objective function of the plane layout problem of tower cranes should not only consider the rent of tower cranes,but also consider the availability of the construction area.The effect of coverage and repeated coverage,using a penalty function to achieve a combination of multiple objectives.Design variables and constraints are normalized.For the established optimization mathematical model,an intelligent optimization algorithm with essential parallelism and global convergence is used to solve it.Finally,the method established in this paper is used to analyze and solve the problem of optimal layout of group towers in a practical project.Numerical examples show that the method proposed in this paper is usable and effective.